Mathematical Description
The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is
where k is the wavenumber,
is the angular frequency of the wave, is an orthogonal matrix whose columns span the transverse x-y plane and is the speed of light.
Here
is the amplitude of the field and
is the Jones vector in the x-y plane.
If is rotated by radians with respect to and the x amplitude equals the y amplitude the wave is circularly polarized. The Jones vector is
where the plus sign indicates left circular polarization and the minus sign indicates right circular polarization. In the case of circular polarization, the electric field vector of constant magnitude rotates in the x-y plane.
If basis vectors are defined such that
and
then the polarization state can be written in the "R-L basis" as
where
and
Read more about this topic: Circular Polarization
Famous quotes containing the words mathematical and/or description:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.”
—Willard Van Orman Quine (b. 1908)